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Fractional diffusion equation with new fractional operator
Alexandria Engineering Journal ( IF 6.8 ) Pub Date : 2020-05-14 , DOI: 10.1016/j.aej.2020.03.027
Ndolane Sene

A new fractional operator with Rabotnov fractional exponential kernel was recently introduced in the literature. In this paper, we consider the fractional diffusion equation in the context of this new fractional operator. We determine the form of the analytical solution and the displacement of the fractional diffusion equation generated by this new fractional operator. In other words, this paper is an application of the fractional derivative with Rabotnow exponential kernel into the diffusion processes. We discuss the results of this paper physically. We make some comparison studies between the results generated by this new operator and those obtained with the fractional derivatives with the singular kernel. We illustrate the main findings of this work by graphical representations of the obtained solution.



中文翻译:

具有新分数算子的分数阶扩散方程

最近在文献中引入了带有Rabotnov分数指数核的新分数算子。在本文中,我们在此新的分数算子的上下文中考虑了分数扩散方程。我们确定解析解的形式以及由该新分数运算符生成的分数扩散方程的位移。换句话说,本文将具有Rabotnow指数核的分数导数应用于扩散过程。我们将实际讨论本文的结果。我们对这个新算子产生的结果与奇异核分数分数导数获得的结果进行了比较研究。我们通过获得的解决方案的图形表示来说明这项工作的主要发现。

更新日期:2020-05-14
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